Suppose that the yt series follows the model yt = yt􀀀1 + "t with "t _ WN(_2 " ). Is yt stationary? If this sequence is not stationary, propose a transformation to induce stationarity. 2.39 Suppose...

Suppose that the yt series follows the model yt = yt􀀀1 + "t with

"t _ WN(_2

" ). Is yt stationary? If this sequence is not stationary, propose a

transformation to induce stationarity.

2.39 Suppose that the series fytg is modeled by yt = _t + xt; where _t =

_t􀀀1 + "t is not observable and xt = !t 􀀀 _!t􀀀1. Assume that "t _ WN(_2 !t _ WN(_2!

); and Cov("t; !s) = 0 for all (t; s). Please answer the following

questions:

(a) What is the mean and the variance of yt?

(b) Is yt stationary?

(c) If part (b) is true, what is the autocovariance function of yt?

(d) If part (b) is false, suggest an appropriate transformation to induce stationarity

in yt. Then, calculate the mean and autocovariance function

of the transformed stationary series.